PHY062 · Modern Physics · Class 12 + College
Radioactive decay
Objective: To model radioactive decay digitally and see that the number of undecayed nuclei falls exponentially.
🧰 Apparatus
- (Digital only) simulated sample of nuclei
- Dice or coins for a classroom model
- Graph paper
📐 Formulas and SI units
N = N₀ e^(−λt)
A = λN (Bq)
💡 Theory
Each nucleus has the same chance of decaying per second, λ, and no way to know which one will go next. So the number left falls by the same fraction in each equal time: N = N₀e^(−λt). The activity A = λN falls in the same way.
🪜 Procedure
- Set N₀ and λ.
- Step the time forward and record N.
- Plot N against t; check it is an exponential curve.
- Plot ln N against t; the slope is −λ.
- Classroom model: roll 100 dice, remove the sixes each throw, and record the number left.
📋 Observations Simulated values
✅ Result and conclusion
1000 nuclei with λ = 0.1 /s leave 368 after 10 s; the activity has dropped from 100 Bq to 37 Bq.
🔬 In a real lab
Real counts fluctuate randomly (± √N), so small samples give jagged curves; large samples follow the exponential closely.
⚠️ Safety
This experiment is digital only. Radioactive sources are not used in school labs here; dice or coins model the randomness safely.
❓ Quick check
1. Which decays next can be predicted?
2. The graph of N against t is…
3. Activity is measured in…
🏋️ Practice
EasyN₀ = 800, λ = 0.1 /s, t = 10 s. N?
Answer: ≈ 294
MediumActivity of 500 nuclei with λ = 0.02 /s?
Answer: 10 Bq
ChallengeWhy do dice model decay well?
Answer: Each die has a fixed chance per throw, like each nucleus